Language Sciences 37 (2013) 136–146 Contents lists available at SciVerse ScienceDirect Language Sciences journal homepage: www.elsevier.com/locate/langsci New methods for analyzingView metadata, case citation and and similar adposition papers at core.ac.uk meaning brought to you by CORE ⇑ provided by Elsevier - Publisher Connector Erkki Luuk Institute of Computer Science, University of Tartu, Postimaja pk 149, Tartu 51004, Estonia article info abstract Article history: The paper proposes two new methods for analyzing case and adposition meaning. The Received 13 September 2011 method for analyzing case and adposition semantics is based on an analysis of semes Received in revised form 15 June 2012 (semantic components) as arguments and predicates in a higher-order logic. The method Accepted 13 August 2012 for case and adposition pragmatics is based on an analysis of case and adposition functions Available online 16 November 2012 as a series of functional derivations. The methods are complementary, cross-linguistically universal and allow for cross-category generalizations. A thorough discussion of the meth- Keywords: ods (including comparisons with earlier ones), formal definitions of case/adposition mean- Case ings and a variety of examples are provided. Adposition Semantics Ó 2012 Elsevier Ltd. Open access under CC BY-NC-ND license. Pragmatics Formal methods Higher-order logic 1. Introduction 1.1. Case and adposition Case is a system for marking dependents for the type of relationship they bear to their heads (Blake, 2001, p. 1). The head is usually the head of the clause (frequently although not necessarily (Luuk, 2010) a finite V) but could also be e.g. the head of possessive phrase. The dependents are usually (but again not necessarily) nominals, interpreted here as the set of {N, ADJ, PRO}. Case and adposition, while formally different (ADP is a word and CAS an affix), are partly co-extensive semantically and pragmatically (Blake, 2001; Butt, 2006). However, there is probably no total functional overlap. I am not sure that there would be languages with adpositional equivalents of ABS or ERG. Still, this is more due to the parsimony of grammar than for semantic reasons. It is easier to make the basic distinction between S and DO with CAS or word order than to have separate words for this. Thus, we can be reasonably confident that CAS and ADP are functionally co-extensive and that a universal semantic analysis of cases would also apply to adpositions and vice versa. However, as a rule of thumb, there are more adpositions than cases in a language. This phenomenon has its roots in the usage frequency and the parsimony related to it. Words are more costly than affixes to produce and parse, so it is optimal to have affixes for more and words for less frequently used meanings (cf. Lestrade, 2010). Correspondingly, the functions of adpositions tend to be narrower than the functions of cases. Thus, as a rule, adpositions are defined more narrowly than cases over (roughly) the same semantic domain. In other respects they are clearly distinct. CAS is an affix, which is a type of morpheme, and morphemes are form-meaning pairs. Thus, CAS is a form-meaning pair where the form and sometimes also the meaning component systematically differs from that of adposition, which is a word, frequently (but not necessarily) another type of morpheme. Below are a few examples of adpositions and cases in different languages: ⇑ Tel.: +372 58896309. E-mail address: [email protected] 0388-0001 Ó 2012 Elsevier Ltd. Open access under CC BY-NC-ND license. http://dx.doi.org/10.1016/j.langsci.2012.08.004 E. Luuk / Language Sciences 37 (2013) 136–146 137 Nomenclature equivalence ! derivation, implication, function or rewrite arrow (depending on the context) := definition x0 the semantics of x x|y|z selection from mutually exclusive categories x, y, z x/y/z selection from mutually nonexclusive categories x, y, z ADJ adjective ABL ablative ABS absolutive ACC accusative ADE adessive ADP adposition ADV adverb ALL allative CAS case cl case landmark cs case subject DAT dative DEL delative DO direct object DP determiner phrase ELA elative ERG ergative GEN genitive ILL illative INE inessive LAT lative LOC locative (case) NOM nominative O object PAR partitive PRO pronoun PUR purposive S subject SEP separative TRL translative V verb (1) Estonian kõnnib (maja-s |maj-ja |maja juurde) walks (house-INE |house-ILL |house to) walks (in|into|to) (a|the) house (2) Swahili yeye anatembea (na|ndani ya) nyumba (s)he walks (to|into) house (s)he walks (to|into) (a|the) house It is evident that cases and adpositions have meanings (as walks (in|into|to) a house do not mean the same, and neither do their Estonian and Swahili counterparts). It can be also observed that CAS and ADP are at least partly co-extensive across languages. 1.2. Semes or semantic components The method we will use in analyzing CAS/ADP semantics is based on semanalysis or component analysis (e.g. Frawley, 1992). Seme or, equivalently, semantic component is defined as the smallest unit of meaning in language, the (non)presence1 of a 1 In a binary system, the nonpresence of a property can imply the presence of another property and vice versa. For example, the nonpresence of PLURAL can imply the presence of SINGULAR. 138 E. Luuk / Language Sciences 37 (2013) 136–146 certain property. For example, the semantics of snow can be analyzed into the set of semantic components {frozen, granulated, water}, while other partitionings are possible. For example, ’water’ could be analyzed further into {substance, tasteless, odorless, transparent, nontoxic, with freezing point at 0 °C at one atmosphere pressure, with boiling point at..., etc.} until sufficient precision has been achieved. For focusing reasons, I will not digress far further into the topic of semes. In the hiearchy of semantic levels, they oc- cupy the second level counting from the most elementary (Luuk, 2008). The third level is occupied by morphemes, while the first one is reserved to semantic primitives (but not in the Wierzbicka (1996, 2000) sense as lexical primitives – semantic primitives do not have to be lexicalized). As an example, one might hypothesize that the semantics of INE involves the following set of semes (at least some of which may be semantic primitives): {SPACE, LOCATION, OBJECT, 3-DIMENSIONAL}. In this case, it is clear that not all these possible semes are semantic primitives (as a semantic primitive cannot, by definition, be reduced to a more elementary meaning). Here, LOCATION, OBJECT, 3-DIMENSIONAL can be re- duced to SPACE, which singles out the latter as the only possible semantic primitive in the set. Semantic primitives in this (non-Wierzbicka) sense are mentioned in passing in Gärdenfors (1998), Langacker (1987), Taylor (1999) and explored to a certain depth in Luuk (2008). 2. The method for analyzing case and adposition semantics 2.1. The method The method I am proposing involves a depiction of case semantics in a higher-order logic with semes and seme com- plexes as predicates and arguments.2 For example, the semantics of ALL and onto can be analyzed as (3) DG(cs,RS(cl)) where DG := goal-determined direction; cs := case subject; cl := case landmark; RS := surface region (see Appendix A). All these are semes or seme complexes (at least two semes in both DG and RS). Thus, a two-place predicate DG taking cs and RS(cl) as arguments. With DG, I am following the observation that directional adpositions can be profiled only with respect to goal (e.g. (in)to, onto), source (from, off) or route (across, via)(Jackendoff, 1983; Zwarts and Winter, 2000). As adposi- tions tend to have more specific meanings than cases, the observation naturally extends to cases. Throughout our walk through case/adposition semantics, cs and cl will appear as the argument variables (’objects’ in the ontology developed in Appendix A), whereas predicates over them are usually constants. It is likely that one will need more lowest-order argu- ments than cs and cl for describing certain other cases and adpositions (e.g. DAT, which subsumes three arguments). There is no fixed limit to the number of lowest-order arguments that the notation can accommodate but, for all practical pur- poses, 3–4 is probably sufficient. The semantics of a CAS or ADP subsumes the number (in our examples, 1–2) and valency (cs, cl) of the arguments, as well as the operation(s) with these. The arguments are semantic not syntactic categories, with names describing their roles: a case subject that usually acts upon, is oriented or moves to(wards), from or via a case land- mark (in a 2-argument scenario). A straightforward semantic interpretation is given by the assignment hierarchy, which for (3) is (4) cs>DG>RS>cl in (other) words, a case subject is assigned a direction and goal, which is assigned a surface region, which is assigned a case landmark. For simplicity, > can be omitted, yielding (5) csDGRScl Observe that (5) is an infix notation3 of (3). Thus, the semantic interpretation of a case or adposition is given by the infix nota- tion of its predicate formula. 2.2. Examples 2.2.1. Allative (6) John puts a vase on(to) the table 2 Differently from first- and second-order logics, higher-order logics allows for predicates as arguments of other (higher-order) predicates. For example, P(K(x)) is a formula of higher-order logic (with arguments in brackets, predicates in front of the brackets, capital letters denoting predicates and small letters the arguments that are not predicates). Thus, K is the lower-order predicate as compared to P, and x is the lower-order argument as compared to K(x).